Ph.D. Mathematics

Introduction

For the award of Ph.D. Mathematics degree, candidates will be required to complete 18 credit hours of coursework along with completion and successful defense of the research thesis. Moreover, the candidate will have to publish at least one paper out of his/her thesis. The minimum duration of the program will be 03 years (extendable up to 8 years) subject to approval by the competent authority.

Note

Research thesis will be got evaluated from three reputed experts in Mathematics (01 from Pakistan and 02 from foreign HEC listed countries)

Eligibility Criteria

Have an MS/M.Phil. (Mathematics)/Equivalent degree in 1^st Division or minimum CGPA 3.00 out of 4.00
Have passed GRE Mathematics (International) with 60% marks or ISP admission test with 60% marks
Have pass an interview conducted by the Department of Mathematics

Scheme of Studies for Ph.D. Mathematics Program

Courses
Elective I	Elective II	Elective III	Elective IV
Elective V	Elective VI	Research Thesis

Elective Courses
Viscous Fluids I	Optimization Theory	Perturbation Method I	Advanced Fixed-Point Theory
Numerical Solutions of Ordinary Differential Equations	Topics in Ring Theory	Numerical Linear Algebra	Approximation Theory and Application
Lattice Theory	Variational Inequalities and Applications	Integral Inequalities	Numerical Solutions of Partial Differential Equations I
Newtonian Fluid Mechanics	Physical Turbulent Flows	Advanced Topics in Graph Theory	Commutative Algebra I
Advanced Topology I	General Relativity	Numerical Optimization	Cryptography
Finite Fields	Fuzzy Logic and its Applications	Parallel Solutions of Partial Differential Equations	MHD and Porous Media
Advanced Modern Algebra with Applications	Representation Theory of Finite Groups	Classical Theory of Fields	Momentum and Thermal Boundary Layer Theory
Stochastic Processes	Convolutions in Geometric function Theory	Semigroup Theory	Financial Mathematics
Mathematical Techniques for Boundary Value Problems	Heat and Mass Transfer	Relativistic Theory of Black Holes	Theory of Abel Grassmann’s Groupoids
Symmetry Methods in Differential Equations	General Linear Models	Rings and Modules	Continuum Mechanics
Numerical Simulation of Reactive Flows	BCI Algebras	Direct and Inverse Problems in Wave Propagation	Commutative Algebra and Algebraic Geometry
Hilbert Space Methods	Fuzzy Graphs and Hypergraphs	Topics in Numerical Analysis I	Topics in Measure Theory
Fractional Calculus	Advanced Partial Differential Equations	Elastodynamics	Fluid and Thermodynamics
Magneto Hydrodynamics	Fractional Differential Equations	Fuzzy Group Theory	Non-Newtonian Fluid Mechanics
Advanced Mathematical Analysis	Advanced Linear Algebra	Advanced Integral Equations	Graph Valuation Theory
Advanced Analytic Dynamics	Advanced Convex Analysis	BCK Algebra Theory	Advanced Numerical Analysis
Theory of Spline Functions	Viscous Fluid II	Representation Theory	Advanced Measure Theory
Complex Analysis of Several Variables	Spectral Methods in Fluid Dynamics	Fuzzy Analysis	Advanced Topics in Graph Valuation Theory
Complexity Theory	Turbulence Modeling	Advanced Differential Equations	Commutative Algebra II
Perturbation Methods II	Boundary Layer Flows	Homological Algebra	Field Extension and Galois Theory
Numerical Solutions of Partial Differential Equations II	General Relativity	Topics in Numerical Analysis II	Near Ring II